We have got Shared Audience and A4T provisions Enabled from Adobe Client Care.And I am able to see the Segments (that I have created in AAM ) under Target Audience Library.Now I would like to list only specific segments from AAM to be shown under AT Audience Library.

1). Can you please update me that Is there any way/option that will enable us to select specific segments to show up under Target Audience Library?.

As I mentioned earlier We have got Shared Audience and A4T provisions Enabled from Adobe Client Care for our company's adobe account. And I am able to see all the Segments (that I have created in AAM ) under Target Audience Library.

1). Can you please update me that Is there any way/option that will enable us to select specific segments in AAM to show up under Target Audience Library?.

Once your account has been setup for Shared audiences all of your AAM segments should be available in Target. There is no need to mark them to go to Target from AAM. In Analtyics however, you do have to mark individual segments you want to make avaialbe in the marketing cloud. These are marked in the segement setup/edit screen within Analyics.